Q$3.$ An oedometer test has been performed on a sample of saturated clay. The time rate of consolidation results for one load increment have been plotted as a$)$ vertical deformation versus log time; and b$)$ vertical deformation versus square root of time, as shown in Figures $2$a and $2$b$.$ During the test, the sample was allowed to drain on both sides $($top and bottom$)$ and its average height was $22\mathrm{.}5$ mm $.$ Determine the coefficient of consolidation $($in $c\frac{m^2}{m}in)$ for this load increment using:

a$).$ Casagrande's Logarithm$-$of$-$Time Fitting Method.

b$).$ Taylor's Square Root of Time Fitting Method.

c$).$ Figure $2c$ shows a plot of the void ratio versus log time for the same load increment. Determine the secondary compression index, $C_{}.$

a$)$ Vertical deformation versus log time test results $($one load increment$)$